1. Field of the Invention
The present invention relates to a stream cipher type enciphering apparatus, deciphering apparatus, keystream generating apparatus and methods for those apparatuses.
2. Description of the Related Art
Stream cipher cryptography, which obtains an exclusive OR of, for example, a binary sequence of a plaintext/ciphertext and a keystream sequence (binary sequence) generated by a common key to thereby generate a ciphertext/plaintext, is considered the most important cryptography at present (references 1 to 5; details on each reference is given later).
The critical problem of the stream cipher cryptography is the difficulty of generating long unpredictable sequences of binary signals (see references 6 to 12) from a short and random key. While linear feedback shift register (LFSR) sequences are often employed in generating binary sequences which are used as keystream sequences, the linear feedback shift register suffers cryptographic weakness (references 2 to 5).
Several nonlinear ergodic maps are known to be excellent choices for a pseudorandom generator (references 19 and 20), and many cryptosystems based on chaotic phenomena have been proposed (references 13 to 16) besides cryptosystems which use the linear feedback shift register. Since such cryptosystems are mostly based on a chaotic real-valued orbit itself and on electronic circuits which handle analog signals, however, their application to digital information communication systems is not easy. Further, since all of the cryptosystems have already been cracked, the use of the cryptosystems is not practical (references 17 and 18). Moreover, important statistical properties, such as correlation functions between the information-bearing signal and its enciphered signal, which should be evaluated in communication systems, have not been theoretically discussed or evaluated.
Further, an enormous amount of block ciphers and stream ciphers has been proposed in various conferences and workshops on cryptologic techniques (e.g., reference 1; details on each reference is given later). Stream cipher cryptography, which obtains an exclusive OR of, for example, a binary sequence of a plaintext/ciphertext and a keystream sequence (binary sequence) generated by a common key to generate a ciphertext/plaintext, is considered the most important cryptography at present (see references 2 to 6). A sequence of independent and identically distributed (i.i.d.) binary random variables which can mimic Bernoulli trials is the best choice for a keystream sequence for a stream cipher. It is well known in the fields of probability theory and ergodic theory that the Rademacher functions (see references 14 to 16) for the dyadic map (Bernoulli map) can produce sequences of i.i.d. binary random variables. The critical problem of the conventional stream cipher cryptography is the difficulty of efficiently generating long unpredictable sequences of binary signals (see references 7 to 13) from a short and random key so that it is not cryptographically secure.
There is the stream cipher which uses the dyadic map. In this system, the binary expansion of an arbitrarily chosen rational seed is the keystream binary sequence itself, which implies that the length of the keystream sequence is equal to the wordlength of the seed after binary expansion. The prior art system cannot therefore permit the dyadic map to generate a chaotic real-valued orbit of long period in a finite-precision computation system.
Since the conventional stream cipher cryptographic techniques are not cryptographically secure as mentioned above, there is a demand for a stream cipher which is based on a new principle and is cryptographically securer.